A generalized ring homomorphisms equation
type: Item
instance of: scholarly article
title: A generalized ring homomorphisms equation
zbMATH Open document ID: 1193.39013
author: Roman Ger
author: Ludwig Reich
published in: Monatshefte für Mathematik
publication date: 2010-02-23T00:00:00Z
review text: Let \(X\) and \(Y\) be two unitary rings. In addition, let \(Y\) be commutative with no zero divisors and \(a, b, c, d, k \in Y\). The authors prove that if the set \(S\) of all solutions \(f: X \to Y\), with \(f(0) = 0\), of the functional equation \[ af(x y) + bf(x) f(y) + cf(x + y) + df(x) + kf(y) = 0 \] is nonempty, then \(k = d = -c\). The main result is a description of the set \(S\) in all possible cases of constants \(a\), \(b\), and \(c\).
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 5674287
zbMATH Keywords: ring homomorphism
zbMATH Keywords: additivity and multiplicativity
zbMATH Keywords: functional equations of Dhombres and Alzer
zbMATH Keywords: unitary rings
reviewed by: Andrzej Smajdor
MaRDI profile type: Publication
full work available at URL: s00605-009-0173-4
OpenAlex ID: W2047337193
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DOI: 10.1007/S00605-009-0173-4
description: scientific article; zbMATH DE number 5674287